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14a^3- 3/a^2=426     [ I'll use "x" instead of "a" ]

14^x^3 -3/x^2 - 426 = 0      multiply through by x^2

14x^5 - 3 - 426x^2 = 0

14x^5 - 426x^2 - 3 = 0

This does not have an algebraic solution, DP   [ or, at least, I don't think that it does ]

There is only one real root at x = a  ≈ 3.12

There are also   4 complex roots

Here is the graph and solution  found by WolframAlpha :

https://www.wolframalpha.com/input/?i=14x%5E5+-+3+-+426x%5E2+%3D+0

16/n^2 * 2.352 = 425.32

Divide both sides by 2.352

16/n^2 = 425.32 / 2.352    and we can write

n^2 /16 = 2.352 / 425.32    multiply both sides by 16

n^2 =   16*2.352 / 425.32     take both roots 

n = ±√ [ 16* 2.352 / 425.32]  ≈   ± 0.297

Here is the graph :  https://www.wolframalpha.com/input/?i=16%2Fn%5E2%C2%A0*+2.352+%3D+425.32